function L2=Lemma2(x)
    global alpha rho L K I var kappa;
    PIPU=x;
    lambar = L*PIPU-(L-1)*alpha*var*(1-rho)/(I-2);
    vbar = alpha*var*(1-rho)/(kappa*lambar+alpha*var*(1-rho));
    ret = alpha*var/(I-2)+alpha*var*rho/(I-2)*(K/((K-L)*((1+(K*vbar-1)*rho)/(1+(K-1)*rho))^2+L)-1);

L2 = ret-PIPU;